Final answer:
The question relates to the crystalline structure of a metal in solid-state physics, specifically a two-dimensional metal with a simple rectangular lattice. The concept of the unit cell, such as the simple cubic lattice where each cell contains one atom, helps in understanding the arrangement and properties of the metal.
Step-by-step explanation:
The student's question deals with the structure of a two-dimensional metal, which has a simple rectangular primitive cell with lattice constants a= 1.5 Å and b=3 Å, and contains one atom per unit cell with one electron per atom. This concept is part of solid-state physics, a branch of physics that describes the physical properties of solids, particularly the electron and atomic structure of crystalline materials.
Crystalline solids like metals have atoms arranged in a regular pattern, which is best characterized by the unit cell. The unit cell is the simplest repeating unit in the lattice structure and determines the metal's properties. The most common metal crystal geometries include simple cubic, body-centered cubic, and face-centered cubic structures. In a simple cubic lattice, each unit cell contains one atom, based on the fact that each of the eight corners of the cube shares its atom with seven other unit cells, hence contributing one-eighth of an atom to each unit cell.
In the context of the question asked, understanding the lattice structure and how unit cells repeat to form the solid is crucial to explaining the physical properties of the mentioned two-dimensional metal solid with a simple rectangular lattice.